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Comparative study of homogenization techniques for evaluating the bearing capacity of bimsoils under shallow foundations

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COMPUTERS AND GEOTECHNICS 2023年 164卷

作者： Montoya-Noguera, Silvana Lopez-Caballero, Fernando Univ EAFIT Sch Appl Sci & Engn Appl Mech Res Grp Medellin 050022 Antioquia Colombia Univ Paris Saclay CentraleSupelec Lab Méc Paris Saclay ENS Paris Saclay F-91190 Gif Sur Yvette France

Bimsoils, characterized by discrete blocks within a finer-grained matrix, pose challenges in evaluating the bearing capacity of shallow foundations due to their spatial variability. To address this, a binary random field coupled with a Finite-Element model is used to simulate the variability of bimsoils. This study focuses on investigating the effect of the blocks spatial fraction (y), the isotropic and anisotropic spatial correlations, and the undrained shear strength (c,,) ratio between the matrix and the blocks. The results reveal that the coefficients of variation (CV) for the bearing capacity (q,,), at a given y, reach nearly 20% due to the diverse spatial configurations. This dispersion is attributed to the development of distinct failure mechanisms. However, optimizing the local average area used to evaluate y can help reduce these CV values. The average q,, for a given y can be accurately determined using the Bruggeman symmetric effective medium (BEM) equation, ensuring safe design compared to traditional homogenization techniques. The BEM equation considers y and the c,, ratio, providing an accurate estimation of bearing capacity for an equivalent homogeneous model suitable for probabilistic analyses.

关键词： Bimsoils Spatial variability binary random fields Bearing capacity Homogenization theories Finite element model

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Numerical modeling of discrete spatial heterogeneity in seismic risk analysis: application to treated ground soil foundation

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GEORISK-ASSESSMENT AND MANAGEMENT OF RISK FOR ENGINEERED SYSTEMS AND GEOHAZARDS 2016年第1期10卷 66-82页

作者： Montoya-Noguera, S. Lopez-Caballero, F. CNRS UMR 8579 MSSMat Lab Cent Supelec F-75700 Paris France

A finite element soil-structure interaction model is coupled with a discrete auto-regressive code, in order to analyze the effect of added spatial variability due to soil improvement in seismic risk analysis. The success of soil improvement techniques is related to the effectiveness of the method - that is, how much of the soil is being changed - but also to its efficiency in improving the soil behavior - that is, how much are the liquefaction and liquefaction-induced settlement reduced. As these techniques can add spatial variability to a deposit, it can affect the triggering of liquefaction on the soil and the behavior of the structures above it. In this study, this heterogeneity is modeled as a binary mixture, composed by the original liquefiable sand and the added treated sand. The soil behavior is represented by a fully nonlinear elastoplastic multi-mechanism model. The co-seismic settlements of the structure and the liquefaction of the soil deposit are estimated for different effectiveness levels - measured by mixture fractions - and for different spatial distributions. In general, both very small or very high mixture fractions presented low efficiency as the improvement in the relative settlement was small. Additionally, results show that the interaction between loose and dense deposits is highly dependent on the spatial distribution. Therefore, homogeneous equivalent models will rarely correspond to the average of the heterogeneous response.

关键词： spatial variability seismic liquefaction binary random fields

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Comparison of spatial methods for the assessment of planktonic patches

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ENVIRONMENTAL AND ECOLOGICAL STATISTICS 2006年第2期13卷 163-181页

作者： Diaz-Avalos, Carlos Bulit, Celia Montagnes, David J. S. Univ Nacl Autonoma Mexico Inst Invest Matemat Aplicadas & Sistemas Mexico City 01000 DF Mexico Univ Autonoma Metropolitana Xochimilco Dept Hombre & Ambiente Mexico City 04960 DF Mexico Univ Liverpool Sch Biol Sci Liverpool L69 7ZB Merseyside England

Planktonic patches are defined as areas where the abundance of plankters is above a threshold value tau. The estimation of patch size and shape can be approached using spatial statistical tools, using truncated random fields or indicator random fields as classifiers. In all cases there is the risk of false positive and false negative errors. In this paper we present the results of a comparative study on the performance of four commonly used methods: conditional simulation and kriging, both in the original measurement units of the data and under an indicator transform. We used a misclassification cost function to compare the four methods. Our results show that conditional simulation in the original measurement units attains the lowest misclassification cost. We also illustrate how the point at which this minimum is attained can be used to chose an optimal cut-off value for binary classification.

关键词： conditional simulation kriging binary random fields patchiness

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Morphological analysis of discrete random shapes

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Journal of Mathematical Imaging and Vision 1992年第2-3期2卷 193-215页

作者： Goutsias, John Image Analysis and Communications Laboratory Department of Electrical and Computer Engineering Johns Hopkins University Baltimore 21218 MD United States

In this paper I discuss a number of theoretical issues regarding the morphological analysis of discrete random shapes by means of Matheron's random set theory. I revisit this theory by limiting myself to the discrete case, since most image data are available in a discrete form. Although it may seem that the transition from the continuous to the discrete case is straightforward (since most of Matheron's theory is general enough to incorporate the discrete case as a special case), this transition is often challenging and full of exciting and, surprisingly, pleasant results. I introduce the concept of the cumulative-distribution functional of a discrete random set and review some fundamental properties of the capacity functional (a fundamental statistical quantity that uniquely defines a random set and relates random set theory to mathematical morphology). In analogy to a recent result and under a natural boundness condition, I show that there exists a one-to-one correspondence between the probability-mass function of a discrete binary random field and the corresponding cumulative-distribution functional. The relationship between the cumulative-distribution functional and the capacity functional of a discrete random set is also established. The cumulative-distribution and capacity functionals are related to the higher-order moments of a discrete binary random field, and, therefore, their computation is equivalent to computing these moments. A brief discussion of how to perform such computations for a certain class of discrete random sets is provided. The capacity functional of a morphologically transformed, continuous random set cannot be associated to the capacity functional of the random set itself, except in the case of dilation. I show that the derivation of such an association is possible in the discrete case and for the cases of dilation and erosion and more complicated morphological transformations, such as opening and closing. These relationships are then used

关键词： binary random fields discrete random shapes mathematical morphology random set theory shape analysis

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